# Load Required Libraries
library(tidycensus)
library(sf)
library(tigris)
library(tmap)
library(spdep)
library(spatialreg)
library(Boruta)
library(ggplot2)
library(RColorBrewer)
library(plotly)
library(tidyverse)
library(DT)
require(knitr)Integrating Simultaneous Spatial Auto-Regressive Modeling to Estimate Median Home Value: A Case Study of Wyoming
Background
This project applies advanced spatial modeling techniques to explore the spatial distribution of housing values across Wyoming census tracts using data from the 2022 American Community Survey (ACS). The methodology combines geospatial and statistical tools, starting with data preprocessing that involves Min-Max normalization and spatial imputation for handling missing values. Spatial relationships are established through a Queen’s contiguity spatial weights matrix, providing a robust foundation for assessing spatial dependencies. Moran’s I analyses validate significant global and local spatial autocorrelation, while the Boruta feature selection algorithm highlights critical predictors, minimizing multicollinearity and enhancing model reliability. Spatial Autoregressive (SAR) modeling is utilized to assess the impact of economic, demographic, and housing factors on normalized median home values (mhvMm), capturing spatial interactions. Advanced visualization methods, such as Moran’s scatter plots and interactive thematic maps, improve the clarity and accessibility of spatial patterns.
I. Load Required Libraries
The Load Required Libraries section introduces essential R packages for my geospatial and statistical analysis workflow. Packages like tidycensus handle Census data, sf and tigris manage spatial data, and tmap supports mapping. Spatial modeling is performed using spdep and spatialreg, while Boruta aids feature selection. Visualization is enhanced with ggplot2, plotly, and RColorBrewer, and data wrangling is streamlined using tidyverse, ensuring an integrated and efficient analysis process.
II. Set Up Census API Key
This code sets the US Census API Key for accessing Census data. The key is saved with install = TRUE and can be overwritten. Get your API key at the US Census Bureau API page.
# US Census API Key
census_api_key('312248c846fdb30816100611e375688ee60be39f', install = TRUE, overwrite = TRUE)[1] "312248c846fdb30816100611e375688ee60be39f"III. Define Census Variables
This code defines a set of key demographic, housing, and economic variables from the US Census Bureau, selected to develop a Simultaneous Spatial Auto-Regressive Model for estimating median home value at the census tract level in Wyoming.
variables <- c(
# Population & Demographics
t_pop = "B01003_001",
m_age = "B01002_001",
p_coll_de = "B15003_022", # College degree (25+)
p_white = "B03002_003",
# Housing Characteristics
mhv = "B25077_001",
m_rent = "B25064_001",
p_owner = "B25008_003",
h_age = "B25035_001",
m_y_built = "B25037_001",
m_rooms = "B25018_001",
# Income & Employment
m_h_income = "B19013_001",
m_income = "DP03_0062", # Added variable
uemp_rate = "B23025_005",
po_rate = "B17001_002",
# Additional Variables
m_h_year = "B25034_001",
p_t_rate = "B25091_001",
a_h_size = "B25010_001"
)
options(tigris_use_cache = TRUE)IV. Retrieve ACS Data and Preprocess
This process retrieves the 2022 ACS data for Wyoming at the census tract level using the get_acs function, selecting a predefined set of variables. It removes margin of error columns, renames variables for clarity, and transforms the data to CRS 3738. A loop replaces missing values (N/A) with the mean of valid neighboring values from 5 rows before and after. Additionally, a log-transformed version of the median home value (l_mhv) is created. The final dataset is displayed interactively using the datatable function for easy exploration and analysis.
wyoming_data <- get_acs(
geography = "tract",
variables = variables,
state = "WY",
year = 2022,
survey = "acs5",
output = 'wide',
geometry = TRUE
) %>%
select(!ends_with("M")) %>%
rename_with(.fn = ~str_remove(.x, "E$")) %>%
st_transform(wyoming_data, crs = 3738)
# Replace N/A values with neighbors' mean (5 neighbors before & after)
for (col in 2:(ncol(wyoming_data)-1)) { # Skip first and last columns
for (i in 1:nrow(wyoming_data)) {
# Check if the value at row i, column col is NA
if (is.na(wyoming_data[i, col][[1]])) {
# Define the range for neighbors (before and after the current row)
start_index <- max(1, i - 5)
end_index <- min(nrow(wyoming_data), i + 5)
# Extract neighbor values, including valid non-NA values
neighbor_values <- wyoming_data[start_index:end_index, col][[1]]
# Filter out NA values
valid_neighbors <- neighbor_values[!is.na(neighbor_values)]
# Replace NA with the mean of valid neighbors if available
if (length(valid_neighbors) > 0) {
wyoming_data[i, col] <- mean(valid_neighbors)
}
}
}
}
# Create log-transformed variable for median home value
l_wyoming_mhv <- wyoming_data %>%
mutate(l_mhv = log10(mhv))
# Render the interactive table
datatable(
l_wyoming_mhv,
options = list(
pageLength = 5, # Number of rows per page
autoWidth = TRUE, # Automatically adjust column width
scrollX = TRUE, # Enable horizontal scrolling
dom = 'Bfrtip', # Include search box, pagination, and more
buttons = c('csv', 'excel', 'pdf', 'print'), # Export options
responsive = TRUE # Make the table responsive
),
extensions = c('Buttons'), # Add buttons for exporting
rownames = FALSE # Hide row names
)V. Visualization: Median Home Value Distribution
This analysis constructs a histogram to examine the distribution of median home values (mhv) in Wyoming using ggplot2. The data is divided into 100 bins with a navy color scheme, and the plot features a minimalistic theme and clear axis labels. To enable interactive exploration, the plot is enhanced with ggplotly.
# Plotting
plot = ggplot(wyoming_data, aes(x = mhv))+
geom_histogram(alpha = 0.5, fill = "navy", color = "navy",
bins = 100) +
theme_minimal() +
scale_x_continuous() +
labs(x = "Median home value")
# Interactive Plot
ggplotly(plot)Visualization with Log Median Home Value
The analysis begins by visualizing the distribution of log-transformed median home values (l_mhv) in Wyoming. Using ggplot2, a histogram with 100 bins is created, employing a navy color scheme for visual clarity. The plot is presented with a minimalistic theme, and labeled for better understanding. To enhance interactivity, ggplotly is used for dynamic exploration of the data.
# Original Visualization: Without Normalization
plot <- ggplot(l_wyoming_mhv, aes(x = l_mhv) ) +
geom_histogram(alpha = 0.5, fill = "navy", color = "navy", bins = 100) +
theme_minimal() +
scale_x_continuous() +
labs(x = "Median Home Value")
ggplotly(plot)VI. Data Normalization: Min-Max
To standardize the dataset, Min-Max normalization is applied to the numeric columns of the Wyoming data. Using mutate, values are rescaled to a range between 0 and 1, excluding the last column. The transformed variables are renamed with a “Mm” suffix for clarity. The geometry is then re-attached, and the result is converted back into an sf object. The final dataset is displayed interactively with datatable for easy exploration.
# Min-Max Normalization
normalized_minmax <- wyoming_data %>%
st_drop_geometry() %>%
mutate(across(where(is.numeric) & !last_col(), ~ (.-min(.))/(max(.)-min(.)))) %>%
rename_with(~ paste0(., "Mm"), where(is.numeric)) %>%
bind_cols(st_geometry(wyoming_data)) %>%
st_as_sf()
# Render the interactive table
datatable(
l_wyoming_mhv,
options = list(
pageLength = 5, # Number of rows per page
autoWidth = TRUE, # Automatically adjust column width
scrollX = TRUE, # Enable horizontal scrolling
dom = 'Bfrtip', # Include search box, pagination, and more
buttons = c('csv', 'excel', 'pdf', 'print'), # Export options
responsive = TRUE # Make the table responsive
),
extensions = c('Buttons'), # Add buttons for exporting
rownames = FALSE # Hide row names
) # Add scrollable box for large tablesVII. Make a Choropleth Map for the Median Home Value Distribution
This code visualizes the normalized median home values (mhvMm) across Wyoming’s census tracts using the tmap package in interactive view mode. The map applies a YlGnBu color palette, representing the data with semi-transparent polygons.This approach offers an informative and visually appealing spatial representation of median home values.
# first let's change the visualization mode as view
tmap_mode('view')
tm_shape(normalized_minmax) +
tm_polygons(
col = "mhvMm", # Column for Median Home Value
palette = "YlGnBu", # Sequential color palette
title = "Median Home Value",
alpha = 0.6 # Transparency
) +
tm_layout(
main.title = "Median Home Value in Wyoming by Census Tract",
main.title.size = 1.3,
main.title.fontface = "bold",
main.title.position = c(0.1, 0.2), # Adjust title position
panel.label.size = 0.8, # Panel label text size
inner.margins = c(0.05, 0.02, 0.08, 0.02),
outer.margins = c(0.05, 0.05, 0.1, 0.1)
) +
tm_borders(
col = "gray",
lwd = 0.08 # Border thickness
) +
tm_scale_bar(
position = c(0.55, 0.01), # Centered at bottom of map
text.size = 0.5, # Scale bar text size
lwd = 0.5 # Scale bar line thickness
) VIII. Construct Spatial Weight Matrix
This code constructs a Queen’s contiguity neighborhood structure using poly2nb, identifying neighbors based on shared edges or vertices. The nb2listw function then creates a row-standardized spatial weights matrix, ensuring each tract’s weights sum to 1, enabling spatial dependence analysis while handling tracts with no neighbors (zero.policy = TRUE).
# Create Queen's neighborhood structure and row-standardized weights
nqueen <- poly2nb(normalized_minmax, queen = TRUE)
nqueenw <- nb2listw(nqueen, style = 'W', zero.policy = TRUE)IX. Visualizing the Neighboring Structure at Census Tract Level
This code visualizes the spatial relationships between Wyoming census tracts using a Queen’s contiguity neighboring structure. Geometric centroids are calculated for each tract, and red lines connect neighboring centroids to represent adjacency. Polygons are styled with light gray fills and borders, and centroids are marked as blue dots. An interactive map is created using the tmap package in “view” mode, incorporating a Leaflet basemap for dynamic exploration. The map includes popups displaying tract information, a clean layout with enhanced legends, and an intuitive design to analyze spatial connections and neighborhood structures effectively.
# Extract coordinates for the polygons
coords <- st_coordinates(st_geometry(normalized_minmax))
# Create empty list to store the neighbor lines
neighbor_lines <- list()
# Loop through the neighbors and create lines between centroids
for (i in seq_along(nqueen)) {
for (neighbor_id in nqueen[[i]]) {
# Ensure there are no duplicate neighbor pairs
if (i < neighbor_id) {
# Get the coordinates for the centroids of the current and neighboring polygons
centroid_i <- st_coordinates(st_centroid(normalized_minmax[i, ]))
centroid_neighbor <- st_coordinates(st_centroid(normalized_minmax[neighbor_id, ]))
# Create a linestring geometry from the two centroids
line <- st_sfc(st_linestring(rbind(centroid_i, centroid_neighbor)), crs = st_crs(wyoming_data))
# Append the linestring to the list of neighbor lines
neighbor_lines <- append(neighbor_lines, list(line))
}
}
}
# Combine all the lines into a single 'sf' object
neighbor_lines_sf <- do.call(c, neighbor_lines)
# Calculate centroids for visualization
centroids <- st_centroid(normalized_minmax)
# Convert centroids to sf (if not already in the correct format)
centroids_sf <- st_as_sf(centroids)
# Create the map using tmap
tmap_mode("view") # Set to interactive mode
# Plot the map with Leaflet basemap and advanced styling
tm_shape(normalized_minmax) +
tm_borders(col = "grey", lwd = 2) + # Polygon borders with slight width
tm_fill(col = "lightgray",
alpha = 0.5,
popup.vars = "NAM") +
tm_dots(col = "blue", size = 0.07, legend.show = TRUE, title = "Centroids") + # Centroids in magenta
tm_shape(neighbor_lines_sf) +
tm_lines(col = "red", lwd = 1) + # Neighbor lines in green
tm_layout(
main.title = "Neighboring Structure at Census Tract Level: Wyoming (Queen's)",
main.title.size = 1.5, # Increase title size
main.title.position = c("center", "top"),
legend.title.size = 1.1, # Legend title size
legend.text.size = 0.8, # Legend text size
frame = FALSE, # No frame around the map
fontfamily = "Arial"
) +
tm_basemap("OpenStreetMap") # Adding OpenStreetMap as the Leaflet basemapX. Spatial Autocorrelation Analysis (Moran’s I)
Global Moran’s I is calculated to assess the overall spatial autocorrelation of normalized median home values (mhvMm). Using the moran.test function, the test evaluates whether similar home values are clustered or dispersed across Wyoming census tracts. The Queen’s contiguity spatial weights matrix (nqueenw) is employed to define spatial relationships, with zero.policy = TRUE handling regions without neighbors and na.action = na.exclude addressing missing values. The result quantifies the degree and significance of spatial autocorrelation, providing insights into the spatial structure of home values.
# Global Moran's I Spatial Autocorrelation
gmoran_result <- moran.test(normalized_minmax$ mhvMm, nqueenw, zero.policy = TRUE, na.action = na.exclude)
gmoran_result
Moran I test under randomisation
data: normalized_minmax$mhvMm
weights: nqueenw
Moran I statistic standard deviate = 14.92, p-value < 2.2e-16
alternative hypothesis: greater
sample estimates:
Moran I statistic Expectation Variance
0.735599775 -0.006289308 0.002472600 XI. Moran’s Scatter Plot
This code constructs an interactive Moran’s I scatterplot to analyze spatial autocorrelation in log-transformed median home values (mhvMm) across Wyoming census tracts. Using the row-standardized spatial weights matrix (nqueenw), spatial lags (lagged_mhv) are calculated via lag.listw. A linear regression model captures the relationship between log_mhv and lagged_mhv, with predictions used to plot a trend line. The scatterplot, created with plotly, features interactive points and a regression line, offering a dynamic visualization of spatial dependence and its directional trend.
# Prepare data for Moran's plot
lagged_var <- lag.listw(nqueenw, normalized_minmax$ mhvMm, zero.policy = TRUE)
moran_data <- data.frame(
log_mhv = normalized_minmax$ mhvMm,
lagged_mhv = lagged_var
)
# Linear regression for the scatterplot line
# Prepare data for Moran's plot
lagged_var <- lag.listw(nqueenw, normalized_minmax $ mhvMm, zero.policy = TRUE)
moran_data <- data.frame(
log_mhv = normalized_minmax$ mhvMm,
lagged_mhv = lagged_var
)
# Linear regression for the scatterplot line
fit <- lm(lagged_mhv ~ log_mhv, data = moran_data)
line_data <- data.frame(
log_mhv = seq(min(moran_data$log_mhv), max(moran_data$log_mhv), length.out = 150),
lagged_mhv = predict(fit, newdata = data.frame(log_mhv = seq(min(moran_data$log_mhv), max(moran_data$log_mhv), length.out = 150)))
)
# Create interactive scatterplot with regression line
plot_ly() %>%
add_trace(
data = moran_data,
x = ~log_mhv,
y = ~lagged_mhv,
type = 'scatter',
mode = 'markers',
marker = list(size = 7, color = 'blue'),
hoverinfo = 'text',
text = ~paste("log_mhv: ", round(log_mhv, 2), "<br>Lagged: ", round(lagged_mhv, 2))
) %>%
add_lines(
data = line_data,
x = ~log_mhv,
y = ~lagged_mhv,
line = list(color = 'red', dash = 'solid'),
name = "Trend Line"
) %>%
layout(
title = "Interactive Moran's I Scatterplot",
xaxis = list(title = "Median Home Value (log10)"),
yaxis = list(title = "Spatial Lag of Median Home Value")
)XII. Local Moran’s I (LISA) Analysis and Cluster Mapping
Leveraging Local Moran’s I, this code identifies and visualizes spatial clusters of log-transformed median home values (mhvMm) across Wyoming census tracts. The localmoran function computes local Moran’s I statistics, which are appended to the dataset for classification. Cluster types—High-High, Low-Low, High-Low, and Low-High—are determined based on quadrant analysis of deviations from the mean, with insignificance identified using a 10% significance threshold. An interactive cluster map is created using tmap in view mode. Polygons are colored to represent cluster types, with a custom palette distinguishing significant spatial patterns. Popups display tract information and cluster classification, while the map features a well-designed layout, including adjusted margins, title placement, and a dynamic Leaflet basemap. This visualization highlights localized spatial autocorrelation, aiding in spatial pattern analysis.
lmoran <- localmoran(normalized_minmax$ mhvMm, nqueenw)
# Bind Local Moran's I result to data and classify clusters
normalized_minmax <- cbind(normalized_minmax, lmoran)
# Quadrant Classification
m_log_mhv <- normalized_minmax$ mhvMm - mean(normalized_minmax$ mhvMm)
m_lmoran <- lmoran[, 1] - mean(lmoran[, 1])
signif <- 0.1 # Significance threshold
quadrant <- vector(mode = "numeric", length = nrow(lmoran))
quadrant[m_log_mhv > 0 & m_lmoran > 0] <- 4
quadrant[m_log_mhv < 0 & m_lmoran < 0] <- 1
quadrant[m_log_mhv < 0 & m_lmoran > 0] <- 2
quadrant[m_log_mhv > 0 & m_lmoran < 0] <- 3
quadrant[lmoran[, 5] > signif] <- 0
normalized_minmax$quadrant <- factor(quadrant, levels = c(0, 1, 2, 3, 4),
labels = c("Insignificant", "Low-Low", "Low-High", "High-Low", "High-High"))
# Cluster Map Visualization
colors <- c("white", "blue", rgb(0, 1, 0, alpha = 0.6), rgb(1, 1, 0, alpha = 0.6), "red")
# moran_clusters <-
tmap_mode('view')
tm_shape(normalized_minmax) +
tm_polygons(
col = "quadrant",
palette = colors, # Color palette for clusters
title = "Clusters",
alpha = 0.6,
popup.vars = c("NAM", "quadrant")
) +
tm_layout(
main.title = "Local Moran's I Clusters",
main.title.size = 1.5,
main.title.fontface = "bold",
main.title.position = c(0.25, 0.2),
bg.color = "grey",
panel.label.bg.color = "grey", # Panel label background
panel.label.size = 0.8, # Smaller panel label size
inner.margins = c(0.05, 0.02, 0.08, 0.02), # Adjust margins
outer.margins = c(0.05, 0.05, 0.1, 0.1) # Space for outside elements
) +
tm_borders(
col = "gray",
lwd = 0.08
) +
tm_basemap("OpenStreetMap")XIV Lagrange Multiplier Tests
This code conducts Lagrange Multiplier (LM) tests to diagnose spatial dependence in a linear regression model (model1). The lm.LMtests function evaluates both spatial lag dependence and spatial error dependence using the Queen’s contiguity spatial weights matrix (nqueenw). These tests help determine whether spatial processes significantly affect the dependent variable (mhvMm) or the error terms, providing guidance on whether a spatial lag or spatial error model should be considered for improved model specification. The zero.policy = TRUE parameter ensures compatibility with tracts that have no neighbors.
# Lagrange Multiplier (LM) tests to diagnose spatial dependence in a linear regression model
lm.LMtests(model1, nqueenw, zero.policy = TRUE)
Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial
dependence
data:
model: lm(formula = mhvMm ~ 1, data = normalized_minmax)
test weights: listw
RSerr = 189.39, df = 1, p-value < 2.2e-16XV. Simultaneous Autoregressive (SAR) Modelling
This section applies a Spatial Autoregressive (SAR) model using spautolm to evaluate the influence of demographic, economic, and housing variables on normalized median home values (mhvMm) while accounting for spatial dependence. The model incorporates a Queen’s contiguity spatial weights matrix (nqueenw) to capture spatial interactions. Key predictors include population size, income, housing age, and unemployment rates. The results are summarized with summary() and presented using kable, offering a detailed yet concise overview of variable effects and spatial dependencies in the data.
# SAR Modelling
norm_SAR <- spatialreg::spautolm(
formula = mhvMm ~ t_popMm + m_ageMm + p_coll_deMm + p_whiteMm +
m_rentMm + p_ownerMm + h_ageMm + m_y_builtMm + m_roomsMm +
m_h_incomeMm + uemp_rateMm + po_rateMm + m_h_yearMm + p_t_rateMm +
a_h_sizeMm,
data = normalized_minmax, listw = nqueenw, zero.policy = TRUE
)
sarOut <- summary(norm_SAR)
kable(sarOut$Coef)| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | -0.0635285 | 0.0563675 | -1.1270411 | 0.2597251 |
| t_popMm | 0.1804621 | 0.1539432 | 1.1722646 | 0.2410909 |
| m_ageMm | 0.0460945 | 0.0391390 | 1.1777146 | 0.2389104 |
| p_coll_deMm | -0.0652582 | 0.0500460 | -1.3039649 | 0.1922455 |
| p_whiteMm | 0.0924140 | 0.0911854 | 1.0134731 | 0.3108343 |
| m_rentMm | 0.0123922 | 0.0314337 | 0.3942326 | 0.6934093 |
| p_ownerMm | -0.1151355 | 0.0676852 | -1.7010443 | 0.0889347 |
| h_ageMm | -0.0548328 | 0.1361094 | -0.4028583 | 0.6870524 |
| m_y_builtMm | 0.1277046 | 0.1387328 | 0.9205076 | 0.3573076 |
| m_roomsMm | 0.1368718 | 0.0360890 | 3.7926213 | 0.0001491 |
| m_h_incomeMm | 0.2327282 | 0.0398290 | 5.8431793 | 0.0000000 |
| uemp_rateMm | -0.0137882 | 0.0260543 | -0.5292080 | 0.5966612 |
| po_rateMm | 0.0466576 | 0.0498742 | 0.9355048 | 0.3495282 |
| m_h_yearMm | 0.2503782 | 0.0998996 | 2.5062982 | 0.0122003 |
| p_t_rateMm | -0.4424093 | 0.1091152 | -4.0545138 | 0.0000502 |
| a_h_sizeMm | -0.0648513 | 0.0496560 | -1.3060113 | 0.1915487 |
XVI. Boruta Feature Selection and SAR Modelling
This section addresses place-based multicollinearity by implementing the Boruta feature selection algorithm to identify the most important predictors for modeling normalized median home values (mhvMm). The Boruta algorithm evaluates the relevance of demographic, economic, and housing variables, eliminating unimportant predictors while retaining significant ones. Using the selected features, a Spatial Autoregressive (SAR) model is constructed with spautolm, incorporating the Queen’s contiguity spatial weights matrix (nqueenw) to account for spatial dependence. Key predictors include population size, education levels, rental rates, and housing characteristics. The refined model reduces multicollinearity, improving the robustness of spatial analysis. Results, including coefficients and spatial effects, are summarized with summary() and presented using kable for clear interpretation. This approach ensures a precise and efficient modeling process.
# Prepare data for Boruta
selected_columns <- c( "p_ownerMm", "uemp_rateMm", "a_h_sizeMm", "m_ageMm",
"t_popMm", "p_coll_deMm", "p_whiteMm", "m_rentMm",
"h_ageMm", "m_y_builtMm", "m_roomsMm", "m_h_incomeMm",
"po_rateMm", "m_h_yearMm", "p_t_rateMm")
boruta_data <- normalized_minmax[, selected_columns] %>%
st_drop_geometry() # Drop geometry for Boruta
boruta_data <- as.data.frame(boruta_data) # Ensure it's a data frame
# Run Boruta
set.seed(123)
boruta_result <- Boruta(boruta_data, normalized_minmax$mhvMm, doTrace = 2)
# Display results and retrieve important features
print(boruta_result)Boruta performed 99 iterations in 14.76906 secs.
9 attributes confirmed important: h_ageMm, m_h_incomeMm, m_rentMm,
m_roomsMm, m_y_builtMm and 4 more;
1 attributes confirmed unimportant: uemp_rateMm;
5 tentative attributes left: a_h_sizeMm, m_ageMm, m_h_yearMm,
p_ownerMm, po_rateMm;plot(boruta_result, main = "Boruta Feature Importance", las = 2)
final_features <- getSelectedAttributes(boruta_result, withTentative = TRUE)
SAR_boruta <- spatialreg::spautolm(
formula = mhvMm ~ t_popMm + m_ageMm + p_coll_deMm + p_whiteMm +
m_rentMm + p_ownerMm + h_ageMm + m_y_builtMm + m_roomsMm +
m_h_incomeMm + po_rateMm + m_h_yearMm + p_t_rateMm +
a_h_sizeMm,
data = normalized_minmax, listw = nqueenw, zero.policy = TRUE
)
modOut<- summary(SAR_boruta)
kable(modOut$Coef)| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | -0.0655200 | 0.0559350 | -1.1713598 | 0.2414542 |
| t_popMm | 0.1664299 | 0.1518182 | 1.0962448 | 0.2729717 |
| m_ageMm | 0.0461557 | 0.0391997 | 1.1774511 | 0.2390155 |
| p_coll_deMm | -0.0613599 | 0.0496433 | -1.2360176 | 0.2164520 |
| p_whiteMm | 0.0986101 | 0.0905095 | 1.0894991 | 0.2759338 |
| m_rentMm | 0.0139409 | 0.0313575 | 0.4445783 | 0.6566245 |
| p_ownerMm | -0.1187192 | 0.0674619 | -1.7597966 | 0.0784423 |
| h_ageMm | -0.0615869 | 0.1356552 | -0.4539960 | 0.6498317 |
| m_y_builtMm | 0.1364778 | 0.1378784 | 0.9898417 | 0.3222515 |
| m_roomsMm | 0.1378873 | 0.0360801 | 3.8217049 | 0.0001325 |
| m_h_incomeMm | 0.2344204 | 0.0397686 | 5.8946142 | 0.0000000 |
| po_rateMm | 0.0443472 | 0.0497732 | 0.8909857 | 0.3729368 |
| m_h_yearMm | 0.2579703 | 0.0990762 | 2.6037557 | 0.0092208 |
| p_t_rateMm | -0.4473195 | 0.1089255 | -4.1066571 | 0.0000401 |
| a_h_sizeMm | -0.0674757 | 0.0494775 | -1.3637665 | 0.1726411 |
XVII. Conclusion
This study highlights the importance of spatial socio-econometric modeling in understanding the spatial distribution of median home values in Wyoming.The Spatial Autoregressive (SAR) model, supported by tests like Moran’s I and Lagrange Multiplier, identifies key factors such as household income, housing size, and property tax rates while showing the need to account for spatial connections. The Boruta-refined SAR model creates a strong framework by focusing on important factors and reducing overlap between variables. The results offer useful insights for policymakers and urban planners, helping them make informed decisions to promote fair and balanced regional growth. The use of advanced spatial analysis and interactive visuals makes this approach easy to replicate and valuable for future studies in geospatial research.